6.5 year veteran of Second Life here. I don't see how it would be possible to do this. Linden Dollar balances only exist on the Second Life servers, tied to an account name. Even Virwox itself and the Second Life company account (named "Supply Linden") have account names. To have an account name, you must open an account on Second Life.
A.) If you are transferring Linden dollars from someone else, then yes -- you must register an avatar to receive them before you can send them to VirWoX to convert to BTCs.
B.) If you already have Second Life account and just want to sell your SLLs through VirWoX, then you update your VirWoX account with your avatar id, and then use the VirWox terminal in-game to transfer the SLLs to VirWoX.
C.) If instead you are first buying SLLs from VirWox and only using them to buy bitcoins, then it is all handled within VirWoX's ledger. i.e., SLLs never left VirWox's account. It is just a book entry. And thus you don't need to touch Second Life or register an avatar.